On overlays and minimization diagrams

The overlay of 2 ≤ m ≤ d minimization diagrams of n surfaces in Rd is isomorphic to a substructure of a suitably constructed minimization diagram of mn surfaces in Rd+m−1 . This elementary observation leads to a new bound on the complexity of the overlay of minimization diagrams of collections of dvariate semi-algebraic surfaces, a tight bound on the complexity of the overlay of minimization diagrams of collections of hyperplanes, and faster algorithms for constructing such overlays. Further algorithmic implications are discussed.

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Vladlen Koltun, Micha Sharir
• Keywords: COMPGEOM 2006, Dvariate Semi-algebraic Surfaces, Minimization Diagrams, Mn Surfaces